Aspects of Sobolev-type inequalities / Laurent Saloff-Coste

Auteur: Saloff-Coste, Laurent (1958-) - AuteurType de document: MonographieCollection: London Mathematical Society lecture note series ; 289Langue: anglaisPays: Grande BretagneÉditeur: Cambridge : Cambridge University Press, 2002Description: 1 vol. (X-190 p.) ; 23 cm ISBN: 0521006074 ; br. Résumé: This book focuses on Poincaré, Nash and other Sobolev-type inequalities and their applications to the Laplace and heat diffusion equations on Riemannian manifolds. Applications covered include the ultracontractivity of the heat diffusion semigroup, Gaussian heat kernel bounds, the Rozenblum-Lieb-Cwikel inequality and elliptic and parabolic Harnack inequalities. Emphasis is placed on the role of families of local Poincaré and Sobolev inequalities. The text provides the first self contained account of the equivalence between the uniform parabolic Harnack inequality, on the one hand, and the conjunction of the doubling volume property and Poincaré's inequality on the other. (source : CUP).Bibliographie: Bibliogr. p. 183-188. Index. Sujets MSC: 46E35 Functional analysis -- Linear function spaces and their duals -- Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
46-02 Functional analysis -- Research exposition (monographs, survey articles)
35-02 Partial differential equations -- Research exposition (monographs, survey articles)
58J05 Global analysis, analysis on manifolds -- Partial differential equations on manifolds; differential operators -- Elliptic equations on manifolds, general theory
58J35 Global analysis, analysis on manifolds -- Partial differential equations on manifolds; differential operators -- Heat and other parabolic equation methods
En-ligne: Zentralblatt | MathSciNet | CUP
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Bibliogr. p. 183-188. Index

This book focuses on Poincaré, Nash and other Sobolev-type inequalities and their applications to the Laplace and heat diffusion equations on Riemannian manifolds. Applications covered include the ultracontractivity of the heat diffusion semigroup, Gaussian heat kernel bounds, the Rozenblum-Lieb-Cwikel inequality and elliptic and parabolic Harnack inequalities. Emphasis is placed on the role of families of local Poincaré and Sobolev inequalities. The text provides the first self contained account of the equivalence between the uniform parabolic Harnack inequality, on the one hand, and the conjunction of the doubling volume property and Poincaré's inequality on the other. (source : CUP)

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